my %bias = (1 => 1, 2 => 1);

##</code><code>##

$rand = $k if rand($sum += $v) <= $v; 
# This simplifies to: 
# $rand = 1 if rand(1) <= 1
# this is always true.  That's wrong.

##</code><code>##

my $sum = 0;
$sum += $_ foreach (values %bias);
my $target = rand($sum);
$sum = 0;
while (my ($k, $v) = each %bias) {
    if ($target <= ($sum += $v)) {
        $rand = $k;
        last;
    }
}